The problem of electron motion in intense laser fields and the radiation generated by this motion has been investigated almost as long as the laser has been around. Early investigations centerred on mass shifts in intense electromagnetic fields, and were soon followed by complete solutions of the problem assuming that the laser is CW with constant amplitude. Likewise, insertion device designers use very similar estimates, assuming constant field strength and hence constant mass shift, to estimate flux and brilliance from insertion devices. Unfortunately, as will be shown in this lecture, such results and estimates may be wildly in error in the more realistic situation when the electron is illuminated by a pulsed laser. A theory developed to cover the general case of illumination by an intense pulsed laser is used to show that typical radiation spectra from the interaction of electrons with pulsed lasers are very substantially broadened beyond that expected from the simple constant-mass-shift uncertainty-principal based arguments usually used. The correct result arises by including the ponderomotive effect of the laser beam and the changes in the mass shift throughout the pulse.


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